An Explicit Watson--Ichino Formula with CM Newforms

Abstract

In this paper, we extend the work of to establish an explicit version of Watson-Ichino formula for L(1/2, f ⊗ ad g), where f is a Hecke-Maass form and g is a CM newform. Contents 1. Introduction 1 2. An explicit version of Watson-Ichino Formula 2 3. Local Calculation in the Watson-Ichino Formula 5 3.1. Whittaker models 6 3.2. Whittaker functions for induced representations 6 3.3. Whittaker functions for supercuspidal representations 15 3.4. The adjoint lift of a supercuspidal representation 20 3.5. Local constants in the Watson-Ichino formula 20 Acknowledgements 25 References 25